High-frequency transmission line, antenna and electronic circuit board

ABSTRACT

A high-frequency transmission line in which the alternating-current resistance is low and that is hard to disconnect is provided. A high-frequency transmission line  2  is a high-frequency transmission line  2  to transmit an alternating-current electric signal, and contains metal and carbon nanotube, and the carbon nanotube is unevenly distributed at a central part  6  of a cross-section that is of the high-frequency transmission line  2  and that is perpendicular to a transmission direction of the alternating-current electric signal.

TECHNICAL FIELD

The present invention relates to a high-frequency transmission line, an antenna and an electronic circuit board.

BACKGROUND

In electronic components, transmission lines for the transmission of electric signals are provided. In the recent advanced information age, the frequency band of an alternating-current electric signal that the transmission line transmits has shifted to a high frequency band. For example, the communication frequency band for a portable information terminal ranges from several hundred [MHz] to several [GHz]. In such a high-frequency transmission line to transmit an alternating-current electric signal in a high frequency band, it is required to raise the electric conductivity and to reduce the transmission loss.

Further, because of the thinning of the high-frequency transmission line due to the downsizing of the electric component, the cross-section area of the high-frequency transmission line becomes small, and the alternating-current resistance of the high-frequency transmission line becomes high. The higher the alternating-current resistance of the high-frequency transmission line is, the greater the Joule heat to be generated in the high-frequency transmission line is. The high-frequency transmission line heated by the Joule heat easily disconnects (fuses). Further, the greater the electric power to be supplied to the high-frequency transmission line is, the more easily the high-frequency transmission line disconnects.

In Patent Literature 1, it is disclosed that carbon nanotubes form a network within a conductor pattern and thereby the electric conductivity and electric power durability of the conductor pattern improve.

[Patent Literature 1] International Publication No. WO2011/062072 pamphlet

SUMMARY

However, the inventors discovered that the alternating-current resistance of the conductor pattern is not sufficiently low in the case where the conductor pattern disclosed in Patent Literature 1 transmits the alternating-current electric signal in the high frequency band. Further, the inventors discovered that the conductor pattern disconnects in the case of supplying a great electric power to the conductor pattern disclosed in Patent Literature 1.

The present invention has been made in view of the above circumstances, and has an object to provide a high-frequency transmission line in which the alternating-current resistance is low and that is hard to disconnect, and an antenna and an electronic circuit board that comprise the high-frequency transmission line.

A high-frequency transmission line according to one aspect of the present invention is a high-frequency transmission line to transmit an alternating-current electric signal, the high-frequency transmission line containing metal and carbon nanotube, the carbon nanotube being unevenly distributed at a central part of a cross-section of the high-frequency transmission line, the cross-section being perpendicular to a transmission direction of the alternating-current electric signal.

In a high-frequency transmission line according to one aspect of the present invention, a content rate of the carbon nanotube at the central part may be 0.5 to 20% by volume.

An antenna according to one aspect of the present invention comprises the high-frequency transmission line according to the above one aspect of the present invention.

An electronic circuit board according to one aspect of the present invention comprises the high-frequency transmission line according to the above one aspect of the present invention.

According to the present invention, a high-frequency transmission line in which the alternating-current resistance is low and that is hard to disconnect, and an antenna and an electronic circuit board that comprise the high-frequency transmission line are provided.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a part of an electronic circuit board according to an embodiment of the present invention, and a high-frequency transmission line.

FIG. 2A and FIG. 2B are schematic cross-section views of the high-frequency transmission line in FIG. 1, in the direction perpendicular to the transmission direction of an alternating-current electric signal.

FIG. 3A, FIG. 3B, FIG. 3C and FIG. 3D are schematic views showing a production method for a high-frequency transmission line according to an embodiment of the present invention.

FIG. 4 is a schematic perspective view of a high-frequency transmission line according to another embodiment of the present invention.

FIG. 5 is a graph showing the relation between the frequencies F of alternating-current electric signals to be transmitted by high-frequency transmission lines and the alternating-current resistances R of the high-frequency transmission lines for each frequency F.

DETAILED DESCRIPTION

Hereinafter, a preferable embodiment of the present invention will be described, in some cases, with reference to the drawings. However, the present invention is not limited to the following embodiment at all. Here, in the drawings, to identical or equivalent constituent elements, an identical reference character is assigned.

As shown in FIG. 1, an electronic circuit board 16 according to the embodiment comprises a high-frequency transmission line 2 and a substrate 4. The high-frequency transmission line 2 is provided along a surface of the substrate 4. The high-frequency transmission line 2 transmits an alternating-current electric signal. The linear arrows shown in FIG. 1 are oriented in the transmission direction of the alternating-current electric signal. The frequency F of the alternating-current electric signal may be, for example, 100 [MHz] to 3.0 [GHz]. With both ends of the high-frequency transmission line 2, terminals 10 are electrically connected, respectively. The shape of the high-frequency transmission line 2 has a meander pattern. The high-frequency transmission line 2 may be an antenna (a radiation conductor or an absorption conductor). In the case where the high-frequency transmission line 2 is an antenna, the terminal 10 for power feeding may be electrically connected with one end of the high-frequency transmission line 2, a high-frequency power feeding circuit (not illustrated) may be electrically connected with the terminal 10 for power feeding, and the high-frequency power feeding circuit may be earthed. Here, the shape of the high-frequency transmission line 2 is not limited to the meander pattern. The high-frequency transmission line 2, for example, may have a linear shape, or may have a curved shape.

The thickness of the whole of the high-frequency transmission line 2 is not particularly limited, and for example, may be about 3 to 50 μm. The thickness of the whole of the high-frequency transmission line 2 is the width of the whole of the high-frequency transmission line 2 in the direction perpendicular to the surface of the substrate 4. The width of the whole of the high-frequency transmission line 2 in the direction parallel to the surface of the substrate 4 is not particularly limited, and for example, may be about 10 μm to 30 mm. The line length of the high-frequency transmission line 2 is not particularly limited, and for example, may be about 0.1 to 100 mm.

The high-frequency transmission line 2 contains metal and carbon nanotube. However, the high-frequency transmission line 2 may contain other chemical elements besides metal and carbon.

The metal contained in the high-frequency transmission line 2 may be, for example, at least one member selected from the group consisting of copper, aluminum, silver, gold, platinum, palladium, chromium, titanium and tantalum. The metal contained in the high-frequency transmission line 2 may be an alloy that contains two or more members of the above metals. Among the above metals, copper, relatively, has a high electric conductivity and is inexpensive.

The carbon nanotube contained in the high-frequency transmission line 2 is not particularly limited. The carbon nanotube is configured, for example, from a cylindrically-closed seamless graphene sheet. The carbon nanotube, based on the number of the layers (graphene sheets) configuring this, is classified into a single-wall carbon nanotube (SWCNT) with a one-layer structure, a double-wall carbon nanotube (DWCNT) with a two-layer structure, and a multi-wall carbon nanotube (MWCNT) with a structure configured by three or more layers. In other words, the MWCNT has a structure in which a plurality of cylindrically-closed graphene sheets are laminated in a nested manner. The carbon nanotube may be at least one member selected from the group consisting of the SWCNT, the DWCNT and the MWCNT. The carbon nanotube may have a linear shape. The carbon nanotube may be bent. At the bending part of the carbon nanotube or the closing part of the cross-section of the carbon nanotube, a ring (for example, a five-membered ring or a seven-membered ring) that is configured by carbon and that is other than a six-membered ring may be present. The carbon nanotube may be chemically modified, and the carbon nanotube may have a functional group. The carbon nanotube is produced by a chemical vapor deposition method, a catalytic vapor deposition method, an arc discharge method or a laser vaporization method, for example.

The diameter (thickness) of the carbon nanotube may be, for example, 1 to 50 nm. The length of the carbon nanotube may be, for example, 100 to 250000 nm. The aspect ratio of the carbon nanotube may be, for example, 100 to 5000. The aspect ratio is the value resulting from dividing the length (nm) of the carbon nanotube by the diameter (nm) of the carbon nanotube.

As shown in FIG. 2A and FIG. 2B, the cross-section of the high-frequency transmission line 2 in the direction perpendicular to the transmission direction of the alternating-current electric signal has a peripheral part 8 and a central part 6. In other words, the perpendicular line (normal line) to the cross-section having the peripheral part 8 and the central part 6 is parallel to the transmission direction of the alternating-current electric signal. The peripheral part 8, which is a part of the high-frequency transmission line 2, is a part where the distance (depth) from the surface of the high-frequency transmission line 2 is 5 μm or less. The peripheral part 8 may be a part where the distance (depth) from the surface of the high-frequency transmission line 2 is 2 μm or less, or 1 μm or less. The central part 6, which is a part of the high-frequency transmission line 2, is a part that is surrounded by the peripheral part 8. As shown in FIG. 2A, the central part 6 does not need to be completely surrounded by the peripheral part 8. The part where the central part 6 is not surrounded by the peripheral part 8 does not need to be on the bottom surface side as shown in FIG. 2A, and for example, may be on a lateral surface side, or may be on the top surface side. As shown in FIG. 2B, the central part 6 may be completely surrounded by the peripheral part 8. Here, the peripheral part 8 continuously extends in the transmission direction of the alternating-current electric signal, and the central part 6 surrounded by the peripheral part 8 also continuously extends in the transmission direction of the alternating-current electric signal.

At the central part 6, many carbon nanotubes are unevenly distributed. That is, many carbon nanotubes are unevenly distributed to the interior of the central part 6 that continuously extends in the transmission direction of the alternating-current electric signal.

In the high-frequency transmission line 2 that transmits the alternating-current electric signal in a high-frequency band, the skin effect occurs. In the skin effect, when the high-frequency electric signal (electric current) flows through the high-frequency transmission line 2, the current density becomes high at the vicinity of the surface of the high-frequency transmission line 2, and becomes low with distance from the surface. Here, the vicinity of the surface of the high-frequency transmission line 2 is, for example, a region where the distance (depth) from the surface of the high-frequency transmission line 2 is 5 μm or less, 2 μm or less, or 1 μm or less. As described above, the peripheral part 8 is a part where the distance (depth) from the surface of the high-frequency transmission line 2 is 5 μm or less, and therefore, the peripheral part 8 can be reworded as the vicinity of the surface of the high-frequency transmission line 2. That is, it can be said that the peripheral part 8 is a part where the electric current concentrates by the skin effect. The higher the frequency of the alternating-current electric signal is, the higher the current density at the peripheral part 8 (the vicinity of the surface) of the high-frequency transmission line 2 is. Therefore, the higher the frequency of the alternating-current electric signal is, the smaller the effective cross-section area of the high-frequency transmission line 2 is and the higher the alternating-current resistance of the high-frequency transmission line 2 is. For this reason, in order to reduce the alternating-current resistance of the high-frequency transmission line 2, it is necessary to raise the electric conductivity of the peripheral part 8 (the vicinity of the surface) of the high-frequency transmission line 2.

However, if the carbon nanotube evenly disperses over the whole of the high-frequency transmission line, not only the metal but also the carbon nanotube are present at the peripheral part (the vicinity of the surface) of the high-frequency transmission line. The electric conductivity of the carbon nanotube is lower than the electric conductivity of a metal simple substance. Therefore, the higher the content rate of the carbon nanotube at the peripheral part is, the more the electric conductivity at the peripheral part decreases. That is, the higher the content rate of the carbon nanotube at the peripheral part is, the more the resistance at the peripheral part increases. In the high-frequency band, by the skin effect, the alternating-current electric signal easily concentrates at the peripheral part, and therefore, by the increase in the resistance at the peripheral part, the alternating-current resistance in the whole of the high-frequency transmission line also easily increases. Further, the Joule heat to be generated at the peripheral part also increases with the increase in the resistance at the peripheral part. The temperature at the peripheral part rises with the increase in the Joule heat generated at the peripheral part. The resistance at the peripheral part and the alternating-current resistance in the whole of the high-frequency transmission line increase with the rise in the temperature at the peripheral part.

If the high-frequency transmission line is composed of only the metal, the electric conductivity of the high-frequency transmission line is higher than the electric conductivity of the high-frequency transmission line containing the carbon nanotube. Further, the Joule heat to be generated in the high-frequency transmission line is less than the Joule heat to be generated in the high-frequency transmission line containing the carbon nanotube. However, the thermal conductivity of the metal simple substance is much lower than the thermal conductivity of the carbon nanotube. Therefore, in the high-frequency transmission line composed of only the metal, the Joule heat is easily accumulated, compared to the high-frequency transmission line containing the carbon nanotube. The high-frequency transmission line is heated by the Joule heat, and the alternating-current resistance of the high-frequency transmission line increases. Further, when the frequency of the alternating-current electric signal increases, the alternating-current resistance of the high-frequency transmission line becomes high by the skin effect, and the Joule heat increases. Since the electric current concentrates at the peripheral part by the skin effect, the Joule heat is easily accumulated at the peripheral part locally. Therefore, in the case where the high-frequency transmission line is composed of only the metal, the increase in the alternating-current resistance due to the Joule heat becomes conspicuous, particularly in the high-frequency band.

On the other hand, in the embodiment, since the carbon nanotube is unevenly distributed at the central part 6, the content rate of the metal at the peripheral part 8 is higher than the content rate of the metal at the central part 6. Therefore, in the embodiment, the electric conductivity at the peripheral part 8 of the high-frequency transmission line 2 is higher than the electric conductivity at the central part 6 of the high-frequency transmission line 2, and the resistance at the peripheral part 8 of the high-frequency transmission line 2 is lower than the resistance at the central part 6 of the high-frequency transmission line 2. In other words, in the embodiment, since the carbon nanotube is unevenly distributed at the central part 6, it is hard for the carbon nanotube to impair the electric conductivity at the peripheral part 8. Therefore, comparing the embodiment and a high-frequency transmission line in which the peripheral part contains the carbon nanotube at a content rate similar to the central part, in the embodiment, both of the resistance at the peripheral part 8 and the alternating-current resistance in the whole of the high-frequency transmission line 2 are low. Further, in the embodiment, even when the current density at the peripheral part 8 increases by the skin effect, since the resistance at the peripheral part 8 is low, the alternating-current resistance of the high-frequency transmission line 2 is hard to increase, and the generation of the Joule heat at the peripheral part is also suppressed.

Further, in the embodiment, the central part 6 at which the carbon nanotube, whose thermal conductivity is higher than the metal, is unevenly distributed functions as a thermal conduction path. That is, the central part 6 radiates heat. Therefore, compared to the high-frequency transmission line composed of only the metal, the Joule heat generated in the high-frequency transmission line 2 according to the embodiment is hard to be accumulated in the high-frequency transmission line 2. Therefore, in the embodiment, the heating of the high-frequency transmission line 2 by the Joule heat is suppressed, and the increase in the alternating-current resistance of the high-frequency transmission line 2 by the heating is also suppressed. Particularly in the high-frequency band, the increase in the alternating-current resistance and the Joule heat by the skin effect is conspicuous, and therefore, the alternating-current resistance of the high-frequency transmission line 2 according to the embodiment, which is excellent in heat radiation property, easily falls below the alternating-current resistance of the high-frequency transmission line composed of only the metal.

As described above, in the embodiment, the increase in the alternating-current resistance and the Joule heat, and the heat accumulation are suppressed, by the synergetic effect of the high electric conductivity at the peripheral part 8 and the high thermal conductivity at the central part 6. Further, in the embodiment, the carbon nanotube unevenly distributed at the central part 6 itself has a high current density resistance property. For these reasons, in the high-frequency transmission line 2 according to the embodiment, the disconnection or the fusion is hard to occur, even when a great electric power is supplied.

In the case where the high-frequency transmission line 2 according to the embodiment is an antenna, the radiation efficiency and absorption efficiency of the antenna according to the embodiment improve compared to the case where the carbon nanotube evenly disperses over the whole of the antenna. Here, the radiation efficiency, for example, is defined as the ratio of the total electric power that the antenna radiates, relative to the total electric power that is supplied to the antenna. The absorption efficiency, for example, is defined as the ratio of the total electric power that the antenna absorbs, relative to the total electric power with which the antenna is irradiated.

The content rate of the carbon nanotube at the central part 6 may be, for example, 0.5 to 20% by volume, relative to the total volume of the central part 6. In the case where the content rate of the carbon nanotube is 0.5% by volume or more, the thermal conductivity at the central part 6 easily becomes high. In the case where the content rate of the carbon nanotube is 20% by volume or less, the increase in the alternating-current resistance in the whole of the high-frequency transmission line 2 that is caused by the relatively low electric conductivity of the carbon nanotube itself is easily suppressed. The central part 6 may contain the above metal, in addition to the carbon nanotube. The content rate of the metal at the central part 6 may be, for example, 80 to 95.5% by volume, relative to the total volume of the central part 6. In the case where the content rate of the metal is 80% by volume or more, the alternating-current resistance in the whole of the high-frequency transmission line 2 is easily reduced by the relatively high electric conductivity of the metal itself at the central part 6. The central part 6 may be composed of only the carbon nanotube.

The content rate of the carbon nanotube at the central part 6 may be measured by the following method, for example. First, the cross-section of the high-frequency transmission line 2 in the direction perpendicular to the transmission direction of the alternating-current electric signal is observed with a seaming electron microscope. The cross-section area of the each carbon nanotube exposed on the central part 6 of this cross-section is measured, and the total value of the cross-section areas of the carbon nanotubes is determined. Further, the area of the whole of the central part 6 exposed on the above cross-section is measured. The content rate of the carbon nanotube at the central part 6 is calculated, by multiplying, by 100, the value resulting from dividing the total value of the cross-section areas of the carbon nanotubes by the value of the area of the whole of the central part 6. That is, the content rate of the carbon nanotube at the central part 6 is equal to the proportion (percentage) of the cross-section area of the carbon nanotube to the whole of the central part 6 exposed on the above cross-section. Here, the content rate of the carbon nanotube at the peripheral part 8 is equal to the proportion (percentage) of the cross-section area of the carbon nanotube to the whole of the peripheral part 8 exposed on the above cross-section.

The thickness d of the peripheral part 8 (the depth of the peripheral part 8) may be 0.1 to 5 μm. In the case where the peripheral part 8 is too thin, the direct-current resistance of the high-frequency transmission line 2 easily increases. In the case where the peripheral part 8 is too thick, the vicinity of the surface of the high-frequency transmission line 2 where the electric current concentrates by the skin effect and the central part are too distant, and therefore, it is difficult to radiate the Joule heat generated at the vicinity of the surface, through the central part 6, which is a thermal conduction path.

Since the electric conductivity of the carbon nanotube is lower than the electric conductivity of the metal simple substance, the lower the content rate of the carbon nanotube at the peripheral part 8 is, the more easily the alternating-current resistance in the whole of the high-frequency transmission line 2 is reduced. In other words, the higher the content rate (volume ratio) of the metal at the peripheral part 8 is, the more easily the alternating-current resistance in the whole of the high-frequency transmission line 2 is reduced. Therefore, it is preferable that the main component of the peripheral part 8 be the above metal. The content rate of the metal at the peripheral part 8 may be more than 95% by volume and 100% by volume or less, or may be 99% by volume or more and 100% by volume or less, relative to the total volume of the peripheral part 8. The peripheral part 8 may be composed of only the above metal. However, a slight amount of carbon nanotube that does not impair the electric conductivity at the peripheral part 8 may be contained in the peripheral part 8.

The substrate 4, for example, may be a semiconductor substrate, or may be an insulating substrate. The substance composing the substrate 4 may be semiconductors such as silicon, gallium arsenide, silicon carbide and gallium nitride, epoxy resin-impregnated glass fibers, dielectric resins such as polycarbonate resin, ABS resin and acrylic resin, or dielectric inorganic compounds such as glass ceramics. The thickness of the substrate 4 is not particularly limited, and for example, may be 50 μm to 2 mm.

Next, a production method for the high-frequency transmission line 2 according to the embodiment will be described below. The following production method is a production method for the high-frequency transmission line 2 having the cross-section shown in FIG. 2B.

As shown in FIG. 3A, a seed layer 8 a is formed on the surface of the substrate 4. For example, in the case where the metal contained in the high-frequency transmission line 2 is copper, the seed layer 8 a composed of copper and chromium is formed. The seed layer 8 a configures a part of the peripheral part 8 of the high-frequency transmission line 2. The seed layer 8 a may be formed by sputtering, for example. By the execution time of the sputtering, it is possible to control the thickness of the seed layer 8 a.

Subsequently, as shown in FIG. 3B, a photoresist 30 is applied to the surface of the seed layer 8 a, Subsequently, the exposure and development of the photoresist is performed, and a concave part 30 a in a meander pattern surrounded by the photoresist 30 is formed.

Subsequently, as shown in FIG. 3C, the central part 6 in the meander pattern is formed in the concave part 30 a. The central part 6 may be formed by the electroplating using a plating solution that contains the metal and the carbon nanotube. That is, the central part 6 may be composed of a plating film that contains the metal and the carbon nanotube. By the content of the carbon nanotube in the electroplating solution, it is possible to control the content rate of the carbon nanotube at the central part 6. By the concentration of the plating solution, the execution time of the plating or the like, it is possible to control the thickness of the central part 6. The plating solution may contain a dispersing agent for dispersing the carbon nanotube. The dispersing agent may be, for example, polystyrene sulfonates, polyvinylpyrrolidone copolymers, water-soluble cellulose, or water-soluble cellulose derivatives.

Subsequently, as shown in FIG. 3D, the photoresist 30, and the seed layer 8 a remaining on the surface of the substrate 4 are removed from the surface of the substrate 4. The peripheral part 8 containing the metal is formed on the surface of the central part 6. The main component of the peripheral part 8 is the metal. The peripheral part 8 may be composed of only the metal. The formation method for the peripheral part 8 may be appropriately selected depending on the kind of the metal composing the peripheral part 8. The formation method for the peripheral part 8 may be, for example, a plating, a sputtering or a chemical vapor deposition (CVD). The plating may be an electroless plating or an electroplating.

By the above processes, the electronic circuit board 16 comprising the substrate 4 and the high-frequency transmission line 2 provided along the surface of the substrate 4 is completed. Here, depending on the formation method for the central part 6 and the peripheral part 8, it is not always necessary to form the seed layer 8 a.

So far, an embodiment of the present invention has been described, but the present invention is not limited to the above embodiment at all.

For example, in the case of producing the high-frequency transmission line 2 having the cross-section shown in FIG. 2A, the seed layer 8 a may be formed by the electroplating or electroless plating using a plating solution that contains copper and carbon nanotube. In this case, the seed layer 8 a configures a part of the central part 6 of the high-frequency transmission line 2.

The formation method for the central part 6 is not limited to the above method. For example, a catalyst component such as gold, silver, copper, iron, cobalt, nickel or tin is attached to the surface of the seed layer 8 a in the concave part 30 a. Subsequently, hydrocarbon gas such as methane or acetylene is decomposed by heat, and the carbon nanotube is grown on the catalyst component. Subsequently, by plating, sputtering or CVD, the metal component is filled into gaps among the carbon nanotubes. By these processes, the central part 6 containing the metal and the carbon nanotube may be formed.

As shown in FIG. 4, the high-frequency transmission line 2 may have a cylindrical shape. That is, the high-frequency transmission line 2 may comprise a cylindrical central part 6 and a cylindrical peripheral part 8 covering the lateral surface of the central part 6. Such a cylindrical high-frequency transmission line 2 may be formed in a through hole or a via hole on an electronic circuit board. The high-frequency transmission line may have a prismatic shape.

Also in a transistor, an IC, a condenser, an inductor, a filter, an electromagnetic shield and the like that comprise the above high-frequency transmission line, the same effect as the above embodiment are achieved.

EXAMPLES

Hereinafter, the content of the present invention will be described in more detail, using examples and comparative examples, but the present invention is not limited to the following examples.

Example 1

A silicon substrate having a thermal oxide film formed on the surface was prepared. The dimensions of the silicon substrate were 30 mm in width×30 mm in length×0.625 in thickness.

By sputtering, a seed layer composed of chromium and copper was formed on the surface of the silicon substrate having thermal oxide film formed. This seed layer configures a part of the peripheral part. The thickness of the seed layer was uniform.

A photoresist was applied to the surface of the seed layer. Subsequently, the exposure and development of the photoresist was performed, and a concave part in a meander pattern was formed.

An electroplating was performed using an electroplating solution containing copper and carbon nanotube. By this electroplating, a central part in the meander pattern that was composed of copper and carbon nanotube was formed in the concave part. The thickness of the central part was uniform. The content rate of the carbon nanotube in the electroplating solution used for the formation of the central part was prepared so as to be 0.1 g/L.

Subsequently, the photoresist and the remaining seed layer were removed from the surface of the silicon substrate. An electroless plating was performed using an electroless plating solution containing copper and not containing carbon nanotube. By this electroless plating, a peripheral part composed of copper was formed on the surface of the central part. The thickness of the peripheral part was uniform.

Through the above processes, a high-frequency transmission line in a meander pattern provided along the surface of the silicon substrate was made. The transmission direction of the alternating-current electric signal on the high-frequency transmission line was the direction parallel to the surface of the silicon substrate. The width of the high-frequency transmission line in the direction parallel to the surface of the silicon substrate was uniform, and was 10 μm. The thickness of the high-frequency transmission line in the direction perpendicular to the surface of the silicon substrate was uniform, and was 10 μm. The line length of the whole of the high-frequency transmission line was 19.7 mm. A cross-section of the high-frequency transmission line in the direction perpendicular to the surface of the silicon substrate (to the transmission direction of the alternating-current electric signal) was observed with a scanning electron microscope. It was confirmed that this cross-section consisted of the rectangular central part 6 and the peripheral part 8 surrounding the four sides of the central part 6 as shown in FIG. 2B. The thickness of the peripheral part 8 was uniform. The thickness of the peripheral part 8 was 2 μm. The content rate of the carbon nanotube at the central part 6 was 0.5% by volume, relative to the total volume of the central part 6. The content rate of the carbon nanotube at the peripheral part 8 was 0% by volume, relative to the total volume of the peripheral part 8. That is, the carbon nanotube was unevenly distributed at the central part 6.

Examples 2 to 5

In Examples 2 to 5, the content rate of the carbon nanotube in the electroplating solution to be used for the formation of the central part was regulated, and the content rate of the carbon nanotube at the central part was controlled to the values shown in Table 1. By the same method as Example 1 except for this point, each high-frequency transmission line in Examples 2 to 5 was made. Except for the content rate of the carbon nanotube at the central part, the dimensions, shape, cross-section configuration and composition of each high-frequency transmission line in Examples 2 to 5 were the same as the high frequency transmission line in Example 1. Here, the content rate of the carbon nanotube in the electroplating solution used for the formation of the central part in Example 2 was 0.2 g/L. The content rate of the carbon nanotube in the electroplating solution used for the formation of the central part in Example 3 was 1.2 g/L. The content rate of the carbon nanotube in the electroplating solution used for the formation of the central part in Example 4 was 2.5 g/L. The content rate of the carbon nanotube in the electroplating solution used for the formation of the central part in Example 5 was 5.0 g/L. The “CNT” shown in Table 1 means the carbon nanotube.

Comparative Example 1

In Comparative Example 1, after the formation of the central part, the peripheral part was formed from the electroplating solution used for the formation of the central part in Example 1. That is, in Comparative Example 1, the peripheral part was formed by not the electroless plating but the electroplating. By the same method as Example 1 except for this point, a high-frequency transmission line in Comparative Example 1 was made. It was confirmed that the content rate of the carbon nanotube at the peripheral part in Comparative Example 1 was the same as the content rate of the carbon nanotube at the central part in Example 1. It was confirmed that the content rate of the carbon nanotube at the central part in Comparative Example 1 was the same as the content rate of the carbon nanotube at the central part in Example 1. That is, it was confirmed that the content rate of the carbon nanotube at the peripheral part in Comparative Example 1 was the same as the content rate of the carbon nanotube at the central part in Comparative Example 1. In other words, it was confirmed that the carbon nanotube was evenly distributed over the whole of the high-frequency transmission line in Comparative Example 1. The dimensions and shape of the high. frequency transmission line in Comparative Example 1 were the same as the high-frequency transmission line in Example 1.

Comparative Example 2

In Comparative Example 2, after the formation of the central part, the peripheral part was formed from the electroplating solution used for the formation of the central part in Example 2. That is, in Comparative Example 2, the peripheral part was formed by not Lie electroless plating but the electroplating. By the same method as Example 2 except for this point, a high-frequency transmission line in Comparative Example 2 was made. It was confirmed that the content rate of the carbon nanotube at the peripheral part in Comparative Example 2 was the same as the content rate of the carbon nanotube at the central part in Example 2. It was confirmed that the content rate of the carbon nanotube at the central part in Comparative Example 2 was the same as the content rate of the carbon nanotube at the central part in Example 2. That is, it was confirmed that the content rate of the carbon nanotube at the peripheral part in Comparative Example 2 was the same as the content rate of the carbon nanotube at the central part in Comparative Example 2. in other words, it was confirmed that the carbon nanotube was evenly distributed over the whole of the high-frequency transmission line in Comparative Example 2. The dimensions and shape of the high-frequency transmission line in Comparative Example 2 were the same as the high-frequency transmission line in Example 2.

Comparative Example 3

In Comparative Example 3, after the formation of the central part, the peripheral part was formed from the electroplating solution used for the formation of the central part in Example 3. That is, in Comparative Example 3, the peripheral part was formed by not the electroless plating but the electroplating. By the same method as Example 3 except for this point, a high-frequency transmission line in Comparative Example 3 was made. It was confirmed that the content rate of the carbon nanotube at the peripheral part in Comparative Example 3 was the same as the content rate of the carbon nanotube at the central part in Example 3. It was confirmed that the content rate of the carbon nanotube at the central part in Comparative Example 3 was the same as the content rate of the carbon nanotube at the central part in Example 3. That is, it was confirmed that the content rate of the carbon nanotube at the peripheral part in Comparative Example 3 was the same as the content rate of the carbon nanotube at the central part in Comparative Example 3. In other words, it was confirmed that the carbon nanotube was evenly distributed over the whole of the high-frequency transmission line in Comparative Example 3. The dimensions and shape of the high-frequency transmission line in Comparative Example 3 were the same as the high-frequency transmission line in Example 3.

Comparative Example 4

In Comparative Example 4, after the formation of the central part, the peripheral part was formed from the electroplating solution used for the formation of the central part in Example 4. That is, in Comparative Example 4, the peripheral part was formed by not the electroless plating but the electroplating. By the same method as Example 4 except for this point, a high-frequency transmission line in Comparative Example 4 was made. It was confirmed that the content rate of the carbon nanotube at the peripheral part in Comparative Example 4 was the same as the content rate of the carbon nanotube at the central part in Example 4. It was confirmed that the content rate of the carbon nanotube at the central part in Comparative Example 4 was the same as the content rate of the carbon nanotube at the central part in Example 4. That is, it was confirmed that the content rate of the carbon nanotube at the peripheral part in Comparative Example 4 was the same as the content rate of the carbon nanotube at the central part in Comparative Example 4. In other words, it was confirmed that the carbon nanotube was evenly distributed over the whole of the high-frequency transmission line in Comparative Example 4. The dimensions and shape of the high-frequency transmission line in Comparative Example 4 were the same as the high-frequency transmission line in Example 4.

Comparative Example 5

In Comparative Example 5, after the formation of the central part, the peripheral part was formed from the electroplating solution used for the formation of the central part in Example 5. That is, in Comparative Example 5, the peripheral part was formed by not the electroless plating but the electroplating. By the same method as Example 5 except for this point, a high-frequency transmission line in Comparative Example 5 was made. It was confirmed that the content rate of the carbon nanotube at the peripheral part in Comparative Example 5 was the same as the content rate of the carbon nanotube at the central part in Example 5, It was confirmed that the content rate of the carbon nanotube at the central part in Comparative Example 5 was the same as the content rate of the carbon nanotube at the central part in Example 5. That is, it was confirmed that the content rate of the carbon nanotube at the peripheral part in Comparative Example 5 was the same as the content rate of the carbon nanotube at the central part in Comparative Example 5. In other words, it was confirmed that the carbon nanotube was evenly distributed over the whole of the high-frequency transmission line in Comparative Example 5. The dimensions and shape of the high-frequency transmission line in Comparative Example 5 were the same as the high-frequency transmission line in Example 5.

Reference Example 1

In Reference Example 1, the central part was formed from an electroplating solution containing copper and not containing carbon nanotube. By the same method as Example 1 except for this point, the high-frequency transmission line in Reference Example 1 was made. The high-frequency transmission line in Reference Example 1 was substantially composed of only copper. That is, the high-frequency transmission line in Reference Example 1 did not contain carbon nanotube. The dimensions and shape of the high-frequency transmission line in Reference Example 1 were the same as the high-frequency transmission line in Example 1.

<Measurement of Alternating-Current Resistance>

Alternating-current electric signals whose frequencies F [GHz] are the values shown in Table 1 were applied to the high-frequency transmission line in Example 1, and the alternating-current resistance R(F) [Ω] of the high-frequency transmission line for each frequency F [GHz] was measured with an impedance analyzer. The alternating-current resistance R(F) is the resistance between one end and the other end of the high-frequency transmission line (meander pattern). By the same method, the alternating-current resistance Rcu(F) [Ω] of the high-frequency transmission line in Reference Example 1 for each frequency F [GHz] was measured. Then, the ratio r(F) of the R(F) to the Rcu(F) for each frequency F [GHz] was determined. The r(F) is expressed by Expression A. The r(F) in Example 1 for each frequency F is shown in Table 1. Here, the electric signal whose frequency F [GHz] is 0 means a direct-current electric signal. Therefore, R(0) is the direct-current resistance of the high-frequency transmission line in Example 1, and Rcu(0) is the direct-current resistance of the high-frequency transmission line in Reference Example 1. r(F)=R(F)/Rcu(F)   (A)

The r(F) in Reference Example 1 shown in Table 1 is defined as Rcu(F)/Rcu(F). Therefore, each r(F) in Reference Example 1 shown in Table 1 is 1.00.

Similarly to Example 1, each r(F) in Examples 2 to 5 and Comparative Examples 1 to 5 was determined. Each r(F) in Examples 2 to 5 and Comparative Examples 1 to 5 is shown in Table 1.

<Measurement of Breakdown Electric Power>

An electric power of 0.1 W was applied to the high-frequency transmission line in Example 1, the electric power was raised in stages, and the electric power (breakdown electric power EP) at the time point when the high-frequency transmission line fused was measured. The electric power application time in each stage was 5 minutes. In the measurement of the breakdown electric power EP, the frequency of the alternating-current electric signal supplied to the high-frequency transmission line in Example 1 was 1.00 [GHz]. By the same method, the breakdown electric power EPcu of the high-frequency transmission line in Reference Example 1 was measured. Then, the ratio r-ep of the breakdown electric power EP in Example 1 to the breakdown electric power EPcu in Reference Example 1 was determined. The r-ep is expressed by Expression B. The r-ep in Example 1 for each frequency F is shown in Table 1. r−ep=EP/EPcu   (B)

The r-ep in Reference Example 1 shown in Table 1 is defined as EPcu/EPcu. Therefore, the r-ep in Reference Example 1 is 1.00.

Similarly to Example 1, each r-ep in Examples 2 to 5 and Comparative Examples 1, to 5 was determined. Each r-ep in Examples 2 to 5 and Comparative Examples 1 to 5 is shown in Table 1. The greater the r-ep is, the harder the high-frequency transmission line is to fuse.

TABLE 1 Content rate of CNT (% by volume) r(F) = R(F)/Rcu(F) Central Peripheral F = F = F = F = F = F = F = F = part part 0[GHz] 0.20[GHz] 0.50[GHz] 0.75[GHz] 1.00[GHz] 1.25[GHz] 1.50[GHz] 2.00[GHz] r-ep Example 1 0.5 0 1.01 1.01 1.00 1.00 1.00 0.99 0.98 0.97 1.80 Comparative 0.5 0.5 1.02 1.02 1.02 1.02 1.01 1.01 1.00 1.00 1.00 Example 1 Example 2 2 0 1.02 1.02 1.01 1.01 1.00 0.99 0.97 0.96 1.85 Comparative 2 2 1.05 1.05 1.04 1.04 1.03 1.02 1.02 1.02 0.95 Example 2 Example 3 8 0 1.07 1.06 1.05 1.03 1.01 0.99 0.97 0.94 1.90 Comparative 8 8 1.16 1.16 1.15 1.15 1.13 1.10 1.09 1.08 0.88 Example 3 Example 4 15 0 1.13 1.12 1.10 1.08 1.05 1.01 0.99 0.95 1.90 Comparative 15 15 1.31 1.31 1.30 1.29 1.28 1.25 1.22 1.20 0.83 Example 4 Example 5 20 0 1.17 1.16 1.14 1.11 1.07 1.03 1.00 0.96 2.00 Comparative 20 20 1.44 1.44 1.43 1.41 1.39 1.34 1.31 1.27 0.77 Example 5 Reference 0 0 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Example 1

Comparison of Example 1, Comparative Example 1 and Reference Example 1

Example 1 and Comparative Example 1, in which the content rates of the carbon nanotubes at the central parts were the same, were compared. It was confirmed that the r(F) in Example 1 was less than the r(F) in Comparative Example 1 for all frequencies F [GHz]. That is, it was confirmed that the alternating-current resistance R(F) in Example 1 was lower than the alternating-current resistance R(F) in Comparative Example 1 for all frequencies F [GHz]. The inventors presume that the low alternating-current resistance R(F) in Example 1 is due to the following factors 1 and 2.

<Factor 1> The content rate of the carbon nanotube in the whole of the high-frequency transmission line in Example 1 is lower compared to Comparative Example 1. Therefore, the electric conductivity in the whole of the high-frequency transmission line in Example 1 is higher than the electric conductivity in the whole of the high-frequency transmission line in Comparative Example 1.

<Factor 2> In both of Example 1 and Comparative Example 1, the higher the frequency F [GHz] is, the more easily the alternating-current electric signal concentrates at the vicinity of the surface of the high-frequency transmission line by the skin effect. Therefore, in both of Example 1 and Comparative Example 1, the higher the frequency F [GHz] is, be more easily the electric conductivity at the vicinity of the surface of the high-frequency transmission line influences the alternating-current resistance in the whole of the high-frequency transmission line. That is, the higher the frequency F [GHz] is, the more easily the alternating-current resistance in the whole of the high-frequency transmission line increases, due to the decrease in the electric conductivity at the vicinity of the surface of the high-frequency transmission line. However, the peripheral part in Example 1 is substantially composed of copper, and does not contain the carbon nanotube. On the other hand, the peripheral part in Comparative Example 1 contains copper and the carbon nanotube. Therefore, the resistance at the peripheral part in Example 1 is lower than the resistance at the peripheral part in Comparative Example 1. Therefore, in the case where the alternating-current electric signal concentrates at the peripheral part of the high-frequency transmission line by the skin effect in the high-frequency band, the transmission of the alternating-current electric signal at the peripheral part in Example 1 is hard to be obstructed, and the generation of the Joule heat at the vicinity of the peripheral part in Example 1 is suppressed.

Example 1 and Reference Example 1 were compared. It was confirmed that the r(F) in Example 1 was less than 1.00 in the case where the frequency F [GHz] was 1.25 [GHz] or higher. That is, it was confirmed that the alternating-current resistance R(F) in Example 1 was lower than the alternating-current resistance Rcu(F) in Reference Example 1 in the case where the frequency F [GHz] was a certain threshold value or higher.

It was confirmed that the r(F) in Example 1 tended to decrease with the increase in the frequency F [GHz]. That is, it was confirmed that the higher the frequency F [GHz] was, the more easily the increase in the alternating-current resistance R(F) in Example 1 was suppressed relative to the increase in the alternating-current resistance Rcu(F) in Reference Example 1.

The inventors presume that the above relation of Example 1 and Reference Example 1 in the high-frequency band is due to the following factor 3.

<Factor 3> In both of Example 1 and Reference Example 1, the higher the frequency F [GHz] is, the more easily the alternating-current electric signal concentrates at the vicinity of the surface of the high-frequency transmission line by the skin effect. Therefore, in both of Example 1 and Reference Example 1, the higher the frequency F [GHz] is, the more easily the electric conductivity at the vicinity of the surface of the high-frequency transmission line influences the alternating-current resistance in the whole of the high-frequency transmission line. That is, the higher the frequency F [GHz] is, the more easily the alternating-current resistance in the whole of the high-frequency transmission line increases, due to the decrease in the electric conductivity at the vicinity of the surface of the high-frequency transmission line, However, in Example 1, the central part 6 at which the carbon nanotube, whose thermal conductivity is higher than copper, is unevenly distributed functions as a thermal conduction path. That is, the central part 6 radiates heat. Therefore, compared to the high-frequency transmission line in Reference Example 1 that is composed of only copper, the Joule heat generated in the high-frequency transmission line in Example 1 is hard to be accumulated in the high-frequency transmission line. Therefore, in Example 1, the heating of the high-frequency transmission line by the Joule heat is suppressed, and the increase in the alternating-current resistance of the high-frequency transmission line by the heating is also suppressed. With the increase in the frequency of the alternating-current electric signal, the alternating-current resistance and the Joule heat increase due to the skin effect. Therefore, the higher the frequency of the alternating-current electric signal is, the more easily the increase in the alternating-current resistance of the high-frequency transmission line in Example 1, which is excellent in heat radiation property, is suppressed, relative to the increase in the alternating-current resistance of the high-frequency transmission line in Reference Example 1, which is composed of only copper.

Comparative Example 1 and Reference Example 1 were compared. It was confirmed that the r(F) in Comparative Example 1 was 1.00 or more for all frequencies F [GHz] That is, it was confirmed that the alternating-current resistance R(F) in Comparative Example 1 was equal to or higher than the alternating-current resistance Rcu(F) in Reference Example 1 for all frequencies F [GHz]. This is because the high-frequency transmission line in Reference Example 1 is substantially composed of only copper, while, in Comparative Example 1, the carbon nanotube, whose electric conductivity is lower than copper, is distributed over the whole of the high-frequency transmission line.

It was confirmed that the r(F) in Comparative Example 1 decreased with the increase in the frequency F [GHz]. In other words, the alternating-current resistance Rcu(F) in Reference Example 1 tended to get close to the alternating-current resistance R(F) in Comparative Example 1, with the increase in the frequency F [GHz]. The inventors presume that this is due to the following factor 4.

<Factor 4> The high-frequency transmission line in Comparative

Example 1 contains the carbon nanotube, and therefore, has the same heat radiation function as Example 1. Therefore, in the high-frequency band in which the alternating-current resistance and the Joule heat increase due to the skin effect, the alternating-current resistance of the high-frequency transmission line in Comparative Example 1, which has heat radiation property, is harder to increase than the alternating-current resistance of the high-frequency transmission line in Reference Example 1, which is composed of only copper.

The alternating-current resistance (R) for each frequency (F) in each of the above-described Example 1, Comparative Example 1 and Reference Example 1 is schematically shown in FIG. 5. Here, the curve of “Pure Cu” shown in FIG. 5 indicates the alternating-current resistance of a high-frequency transmission line composed of only an ideal copper that does not generate heat. That is, the alternating-current resistance of “Pure Cu” is not influenced by the Joule heat, and increases only by the skin effect.

Comparison of Example 2, Comparative Example 2 and Reference Example 1

Example 2 and Comparative Example 2, in which the content rates of the carbon nanotubes at the central parts were the same, were compared. It was confirmed that the r(F) in Example 2 was less than the r(F) in Comparative Example 2 for all frequencies F [GHz]. That is, it was confirmed that the alternating-current resistance R(F) in Example 2 was lower than the alternating-current resistance R(F) in Comparative Example 2 for all frequencies F [GHz]. It was confirmed that the r(F) in Example 2 was less than 1.00 in the case where the frequency F [GHz] was 1.25 [GHz] or higher. That is, it was confirmed that the alternating-current resistance R(F) in Example 2 was lower than the alternating-current resistance Rcu(F) in Reference Example 1 in the case where the frequency F [GHz] was a certain threshold value or higher. It was confirmed that the r(F) in Example 2 tended to decrease with the increase in the frequency F [GHz]. That is, it was confirmed that the higher the frequency F [GHz] was, the more easily the increase in the alternating-current resistance R(F) in Example 2 was suppressed relative to the increase in the alternating-current resistance Rcu(F) in Reference Example 1. It was confirmed that the r(F) in Comparative Example 2 was more than 1.00 for all frequencies F [GHz]. That is, it was confirmed that the alternating-current resistance R(F) in Comparative Example 2 was higher than the alternating-current resistance Rcu(F) in Reference Example 1 for all frequencies F [GHz]. It was confirmed that the r(F) in Comparative Example 2 tended to decrease with the increase in the frequency F [GHz]. That is, it was confirmed that the increase in the alternating-current resistance R(F) in Comparative Example 2 was suppressed more easily than the increase in the alternating-current resistance Rcu(F) in Reference Example 1, with the increase in the frequency F [GHz].

Comparison of Example 3, Comparative Example 3 and Reference Example 1

Example 3 and Comparative Example 3, in which the content rates of the carbon nanotubes at the central parts were the same, were compared. It was confirmed that the r(F) in Example 3 was less than the r(F) in Comparative Example 3 for all frequencies F [GHz]. That is, it was confirmed that the alternating-current resistance R(F) in Example 3 was lower than the alternating-current resistance R(F) in Comparative Example 3 for all frequencies F [GHz]. It was confirmed that the r(F) in Example 3 was less than 1.00 in the case where the frequency F [GHz] was 1.25 [GHz] or higher. That is, it was confirmed that the alternating-current resistance R(F) in Example 3 was lower than the alternating-current resistance Rcu(F) in Reference Example 1 in the case where the frequency F [GHz] was a certain threshold value or higher. It was confirmed that the r(F) in Example 3 tended to decrease with the increase in the frequency F [GHz]. That is, it was confirmed that the higher the frequency F [GHz] was, the more easily the increase in the alternating-current resistance R(F) in Example 3 was suppressed relative to the increase in the alternating-current resistance Rcu(F) in Reference Example 1. It was confirmed that the r(F) in Comparative Example 3 was more than 1.00 for all frequencies F [GHz]. That is, it was confirmed that the alternating-current resistance R(F) in Comparative Example 3 was higher than the alternating-current resistance Rcu(F) in Reference Example 1 for all frequencies F [GHz]. It was confirmed that the r(F) in Comparative Example 3 tended to decrease with the increase in the frequency F [GHz]. That is, it was confirmed that the increase in the alternating-current resistance R(F) in Comparative Example 3 was suppressed more easily than the increase in the alternating-current resistance Rcu(F) in Reference Example 1, with the increase in the frequency F [GHz].

Comparison of Example 4, Comparative Example 4 and Reference Example 1

Example 4 and Comparative Example 4, in which the content rates of the carbon nanotubes at the central parts were the same, were compared. It was confirmed that the r(F) in Example 4 was less than the r(F) in Comparative Example 4 for all frequencies F [GHz]. That is, it was confirmed that the alternating-current resistance R(F) in Example 4 was lower than the alternating-current resistance R(F) in Comparative Example 4 for all frequencies F [GHz]. It was confirmed that the r(F) in Example 4 was less than 1.00 in the case where the frequency F [GHz] was 1.50 [GHz] or higher. That is, it was confirmed that the alternating-current resistance R(F) in Example 4 was lower than the alternating-current resistance Rcu(F) in Reference Example 1 in the case where the frequency F [GHz] was a certain threshold value or higher. It was confirmed that the r(F) in Example 4 tended to decrease with the increase in the frequency F [GHz]. That is, it was confirmed that the higher the frequency F [GHz] was, the more easily the increase in the alternating-current resistance R(F) in Example 4 was suppressed relative to the increase in the alternating-current resistance Rcu(F) in Reference Example 1. It was confirmed that the r(F) in Comparative Example 4 was more than 1.00 for all frequencies F [GHz]. That is, it was confirmed that the alternating-current resistance R(F) in Comparative Example 4 was higher than the alternating-current resistance Rcu(F) in Reference Example 1 for all frequencies F [GHz]. It was confirmed that the r(F) in Comparative Example 4 tended to decrease with the increase in the frequency F [GHz]. That is, it was confirmed that the increase in the alternating-current resistance R(F) in Comparative Example 4 was suppressed more easily than the increase in the alternating-current resistance Rcu(F) in Reference Example 1, with the increase in the frequency F [GHz].

Comparison of Example 5, Comparative Example 5 and Reference Example 1

Example 5 and Comparative Example 5, in which the content rates of the carbon nanotubes at the central parts were the same, were compared. It was confirmed that the r(F) in Example 5 was less than the r(F) in Comparative Example 5 for all frequencies F [GHz]. That is, it was confirmed that the alternating-current resistance R(F) in Example 5 was lower than the alternating-current resistance R(F) in Comparative Example 5 for all frequencies F [GHz]. It was confirmed that the r(F) in Example 5 was less than 1.00 in the case where the frequency F [GHz] was 2.00 [GHz]. That is, it was confirmed that the alternating-current resistance R(F) in Example 5 was lower than the alternating-current resistance Rcu(F) in Reference Example 1 in the case where the frequency F [GHz] was 2.00 [GHz]. It was confirmed that the r(F) in Example 5 tended to decrease with the increase in the frequency F [GHz]. That is, it was confirmed that the higher the frequency F [GHz] was, the more easily the increase in the alternating-current resistance R(F) in Example 5 was suppressed relative to the increase in the alternating-current resistance Rcu(F) in Reference Example 1. It was confirmed that the r(F) in Comparative Example 5 was more than 1.00 for all frequencies F [GHz]. That is, it was confirmed that the alternating-current resistance R(F) in Comparative Example 5 was higher than the alternating-current resistance Rcu(F) in Reference Example 1 for all frequencies F [GHz]. It was confirmed that the r(F) in Comparative Example 5 tended to decrease with the increase in the frequency F [GHz]. That is, it was confirmed that the increase in the alternating-current resistance R(F) in Comparative Example 5 was suppressed more easily than the increase in the alternating-current resistance Rcu(F) in Reference Example 1, with the increase in the frequency F [GHz].

[Evaluation of Breakdown Electric Power]

As shown in Table 1, it was confirmed that the r-ep in all examples was more than 1.00. Further, it was confirmed that the r-ep in all examples was more than the r-ep in all comparative examples. That is, it was confirmed that the breakdown electric powers of the high-frequency transmission lines in all examples were greater than the breakdown electric powers in Reference Example 1 and all comparative examples. That is, it was confirmed that the high-frequency transmission lines in all examples were hard to fuse compared to the high-frequency transmission lines in Reference Example 1 and all comparative examples. The inventors presume that the great breakdown electric powers in all examples are due to the following factor 5.

<Factor 5> In the examples, the increase in the alternating-current resistance and the Joule heat, and the heat accumulation are suppressed, by the synergetic effect of the high electric conductivity at the peripheral part and the high thermal conductivity at the central part. Further, in the examples, the carbon nanotube unevenly distributed at the central part itself has a high current density resistance property. For these reasons, in the high-frequency transmission lines according to the examples, the fusion is hard to occur, even when a great electric power is supplied. On the other hand, in the comparative examples, since the peripheral part contains the carbon nanotube at the same content rate as the central part, the electric conductivity at the peripheral part is lower compared to the examples. Therefore, in the comparative examples, the above synergetic effect is hard to be obtained. The high-frequency transmission line in Reference Example 1, because of containing no carbon nanotube, is lower than the examples in the thermal conductivity in the whole of the high-frequency transmission line, and is inferior to the examples in the current density resistance property in the whole of the high-frequency transmission line.

According to the present invention, a high-frequency transmission line in which the alternating-current resistance is low and that is hard to disconnect, and an antenna and an electronic circuit board that comprise the high-frequency transmission line are provided.

2 . . . high-frequency transmission line (or antenna), 4 . . . substrate, 6 . . . central part, 6 a . . . seed layer, 8 . . . peripheral part, 10 . . . terminal, 16 . . . electronic circuit board, 30 . . . photoresist, 30 a . . . concave part, d . . . thickness of a peripheral part. 

What is claimed is:
 1. A high-frequency transmission line to transmit an alternating-current electric signal, the high-frequency transmission line containing metal and carbon nanotube, the carbon nanotube being unevenly distributed at a central part of a cross-section of the high-frequency transmission line, the cross-section being perpendicular to a transmission direction of the alternating-current electric signal, wherein a content rate of the carbon nanotube at the central part is 0.5% to 20% by volume.
 2. An antenna comprising the high-frequency transmission line according to claim
 1. 3. An electronic circuit board comprising the high-frequency transmission line according to claim
 1. 